Typed Assembly Languages (TALs) are used to validate the safety of machine-language programs. The Foundational Proof-Carrying Code project seeks to verify the soundness of TALs using the smallest possible set of axioms: the axioms of a suitably expressive logic plus a specification of machine semantics. This article proposes general semantic foundations that permit modular proofs of the soundness of TALs. These semantic foundations include Typed Machine Language (TML), a type theory for specifying properties of low-level data with powerful and orthogonal type constructors, and L c , a compositional logic for specifying properties of machine instructions with simplified reasoning about unstructured control flow. Both of these components, whose semantics we specify using higher-order logic, are useful for proving the soundness of TALs. We demonstrate this by using TML and L c to verify the soundness of a low-level, typed assembly language, LTAL, which is the target of our core-ML-to-sparc compiler. To prove the soundness of the TML type system we have successfully applied a new approach, that of step-indexed logical relations . This approach provides the first semantic model for a type system with updatable references to values of impredicative quantified types. Both impredicative polymorphism and mutable references are essential when representing function closures in compilers with typed closure conversion, or when compiling objects to simpler typed primitives.

By combining existing type systems with standard type-based compilation techniques, we describe how to write strongly typed programs that include a function that acts as a t racing garbage collector for the program. Since the garbage collector is an explicit function, we do not need to provide a t rusted garbage collector as a runtime service to manage memory.Since our language is strongly typed, the standard type soundness guarantee "Well typed programs do not go wrong" is extended to include the collector. Our type safety guarantee is non-trivial since not only does it guarantee the type safety of the garbage collector, but it guarantees that the collector preservers the type safety of the program being garbage collected. We describe the technique in detail and report performance measurements for a few microbench-marks as well as sketch the proofs of type soundness for our system.